First, let’s address the misunderstanding. In the mathematical field of probability, there is a theorem called the Law of Large Numbers. It simply states that, as the number of trials increase, the results will approach the expected mean or average value. As for the lottery, this means that eventually all lottery numbers will hit the same number of times. By the way, I totally agree.

The first misunderstanding arises from the words, ‘as the number of samples or trials increase’. Increase to what? Is 50 drawings enough? 100? 1,000? 50,000? The name itself, ‘Law of Large Numbers’, should give you a clue. The second misunderstanding centers around the use of the word ‘approach’. If we are going to ‘approach the expected mean’, how close do we have to get before we are satisfied?

Second, let’s discuss the misapplication. Misunderstanding the theorem results in its misapplication. I’ll show you what I mean by asking the questions that the esambad skeptics forget to ask. How many drawings will it take before the results will approach the expected mean? And, what is the expected mean?

To demonstrate the application of Law of Large Numbers, a two-sided coin is flipped numerous times and the results, either Heads or Tails, are recorded. The intent is to prove that, in a fair game, the number of Heads and Tails, for all intents and purposes, will be equal. It typically requires a few thousand flips before the number of Heads and Tails are within a fraction of 1% of each other.

Lotto Statistics

With regards to the lottery, the skeptic proceeds to apply this theorem but never specifies what the expected value should be nor the number of drawings required. The effect of answering these questions is very telling. To demonstrate, let’s look at some real numbers. For the purposes of this discussion, I’ll use the TX654 lottery.

In the last 336 drawings,(3 years and 3 months) 2016 numbers have been drawn (6×336). Since there are 54 lottery numbers in the hopper, each number should be drawn about 37 times. This is the expected mean. Here is the point where the skeptic gets a migraine. After 336 drawings, the results are nowhere near the expected value of 37, let alone within a fraction of 1%. Some numbers are more than 40% higher than the expected mean and other numbers are more than 35% below the expected mean. What does this imply? Obviously, if we intend to apply the Law of Large Numbers to the lottery, we will have to have many more drawings; a lot more!!!